This paper explains how the Gibbs sampler can be used to perform Bayesian inference on GARCH models. Although the Gibbs sampler is usually based on the analytical knowledge of the full conditional posterior densities, such knowledge is not available in regression models with GARCH errors. We...

In this paper we propose a form of semi-nonparametric regression based on wavelet analysis, and demonstrate its empirical utility in the context of commodity price behavior.

A geometrical setting is constructed, based on Hilbert space, in which the asymptotic properties of estimators can be studied. Estimators are defined in the context of parametrised models, which are treated as submanifolds of an underlying Hilbert manifold, on which a parameter-defining mapping...

We show that, in many circumstances, the size distortion of a bootstrap P value for a test will be one whole order of magnitude smaller than that of the corresponding asymptotic P value. We also show that, at least in the parametric case, the magnitude of the distorsion will depend on the shape...

A unit root test is usually carried out by using the regression test introduced by Dickey and Fuller (1979). Under the null hypothesis the series should be a random walk and a stationary component. This is what is done in additive decompositions between trend and cycle. The paper analyses the...

Dans la pratique, la plupart des statistiques de test ont une distribution de probabilite de forme inconnue. Generalement, on utilise leur loi asymptotique comme approximation de la vraie loi. Mais, si l'echelon dont on dispose n'est pas de taille suffisante cette approximation peut etre de...

Bootstrap tests are tests for which the significance level is calculated by some sort of bootstrap procedure, which may be parametric or nonparametric. We provide a theoretical framework in which to study the size distorsions of bootstrap P values. We show that, in many circumstances, the size...

This paper discusses ways to reduce the bias of consistent estimators that are biased in finite samples. It is necessary only that the bias function, which relates parameter values to bias, should be estimable by computer simulation or by some other method. If so, bias can be reduced or even...

A unit root test is usually carried out by using the regression test introduced by Dickey and Fuller (1979). Under the null hypothesis the series should be a random walk. But a non-stationary series can usually be decomposed into a random walk and a stationary component. This is what is done in...

Most confidence intervals, whether based on asymptotic theory or the bootstrap, are implicitly based on inverting a Wald test. Since Wald test statistics are not invariant under nonlinear reparametrizations of the restrictions they test, confidence intervals based on them are not invariant...